A363511 Number of partitions of [n] having exactly one parity change within their blocks.

0, 0, 1, 2, 6, 18, 61, 210, 778, 3008, 12219, 52268, 231726, 1083012, 5202199, 26307710, 135972580, 738339310, 4081523615, 23649300862, 139096468520, 855529383396, 5329630673249, 34643027568520, 227682351175868, 1558106351450416, 10766192988109009

Offset: 0

Author

Alois P. Heinz, Jun 06 2023

Keywords

• nonn

Examples

			a(4) = 6: 124|3, 12|3|4, 134|2, 1|23|4, 14|2|3, 1|2|34.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Wikipedia, Partition of a set

Crossrefs

Column k=1 of A363493.

Cf. A000110, A124419.

Programs

Maple

b:= proc(n, x, y) option remember; convert(series(
     `if`(n=0, 1, `if`(y=0, 0, expand(b(n-1, y-1, x+1)*y*z))
       +b(n-1, y, x)*x + b(n-1, y, x+1)), z, 2), polynom)
    end:
a:= n-> coeff(b(n, 0$2), z, 1):
seq(a(n), n=0..27);